Novel Coding-Aware Scheme to Minimize Energy Consumption and Time Cost

ABSTRACT

The throughput of a wireless network can be boosted by network coding (NC). The present invention combines NC-aware routing and TDMA-based MAC protocol for energy-efficient design in the wireless network, and provides a method thereof. An optimization model, which is a minimum energy consumption model (MECM), is formulated for minimizing the energy consumption for accomplishing a set of flow transmissions. In particular, based on a set of user traffic-flow demands, a NC-aware traffic-flow assignment that minimizes a total energy consumption of packets delivering to meet the user traffic-flow demands is determined. Thereafter, given the optimal flow assignment, a minimum timeslots model (MTM) which leads to a TDMA-based scheduling strategy at the MAC layer is developed. The MTM is to minimize the total number of timeslots required for transmission under a condition that the NC-aware traffic-flow assignment as already determined is accomplishable.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 62/197,020, filed on Jul. 26, 2015, which isincorporated by reference herein in its entirety.

BACKGROUND

Field of the Invention

The present invention generally relates to routing and scheduling of awireless network. In particular, the present invention relates to atechnique combining routing and scheduling for energy-efficient designof the wireless network, where network coding is used in routing forenergy-efficient communications, and TDMA-based MAC scheduling is usedto minimize the total time cost.

List of References

There follows a list of references that are occasionally cited in thespecification. Each of the disclosures of these references isincorporated by reference herein in its entirety.

-   -   [1] W. Heinzelman, A. Chandrakasan, and H. Balakrishnan,        “Energy-Efficient Communication Protocol for Wireless        Microsensor Networks,” IEEE 33rd Annual Hawaii International        Conference on System Sciences, 2000.    -   [2] C. K. Toh, “Maximum Battery Life Routing to Support        Ubiquitous Mobile Computing in Wireless Ad Hoc Networks,” IEEE        Communications Magazine, vol. 39, no. 6, pp. 138-147, 2001.    -   [3] A. S. K. Mammu, A. Sharma, U. Hernandez, et al, “A Novel        Cluster-Based Energy Efficient Routing in Wireless Sensor        Networks,” IEEE 27th International Conference on Advanced        Information Networking and Applications (AINA), 2013.    -   [4] A. Amokrane, R. Langar, R. Boutaba, et al, “A Green        Framework for Energy Efficient Management in TDMA-based Wireless        Mesh Networks,” IEEE 8th International Conference on Network and        Service Management, 2012.    -   [5] R. Ahlswede, N. Cai, S.-Y. R. Li, et al, “Network        Information Flow,” IEEE Transactions on Information Theory, vol.        46, no. 4, pp. 1204-1216, 2000.    -   [6] A. Keshavarz-Haddadt, and R. Riedi, “Bounds on the Benefit        of Network Coding: Throughput and Energy Saving in Wireless        Networks,” IEEE 27th Conference on Computer Communications,        2008.    -   [7] H. Chang, X. Gao, R. Zong, et al, “Energy-Efficient        Coding-Aware Routing in Energy-Constrained Wireless Network,”        IEEE 2010 international Symposium on Intelligent Signal        Processing and Communication Systems (ISPACS), pp. 1-4, 2010.    -   [8] S. Wang, A. Vasilakos, H. Jiang, et al, “Energy Efficient        Broadcasting Using Network Coding Aware Protocol in Wireless Ad        hoc Network,” IEEE International Conference on Communications,        pp. 1-5, 2011.    -   [9] S. Sengupta, S. Rayanchu, and S. Banerjee, “An Analysis of        Wireless Network Coding for Unicast Sessions: The Case for        Coding-Aware Routing,” IEEE 26th International Conference on        Computer Communications, pp. 1028-1036, 2007.    -   [10] S. Katti, H. Rahul, W. Hu, et al, “XORs in the Air:        Practical Wireless Network Coding,” ACM SIGCOMM Computer        Communication Review, vol. 36, no. 4, pp. 243-254, 2006.    -   [11] J. Liu, D. Goeckel, D. Towsley, “Bounds on the Gain of        Network Coding and Broadcasting in Wireless Networks,” IEEE        26^(th) International Conference on Computer Communications, pp.        724-732, 2007.    -   [12] N. Gaddam, S. A. Gathala, D. Lastine, et al, “Energy        Minimization Through Network Coding for Lifetime Constrained        Wireless Networks,” IEEE 17th International Conference on        Computer Communications and Networks, 2008.    -   [13] K. Xiao, Y. Zhang, G. Feng, et al, “eCOPE: Energy Efficient        Network Coding Scheme in Multi-Rate Wireless Networks,” Wireless        Communications and Networking Conference Workshops (WCNCW) 2013,        pp. 18-23, 2013.    -   [14] A. Amokrane, R. Langar, R. Boutabayz, et al, “Online        Flow-Based Energy Efficient Management in Wireless Mesh        Networks,” Global Communications Conference (GLOBECOM) 2013, pp.        329-335, 2013.    -   [15] R. Wang, Z. Jiang, S. Gao, et al, “Energy-Aware Routing        Algorithms in Software-Defined Networks,” IEEE 15th        International Symposium on A World of Wireless, Mobile and        Multimedia Networks (WoWMoM), pp. 1-6, 2014.    -   [16] D. Couto, D. Aguayo, J. Bicket, et al, “A High Throughput        Path Metric for Wireless sensor Routing,” Wireless Networks        2005, vol. 11, no. 4, pp. 419-434, 2005.

Description of Related Art

During recent years, energy-efficient communication in wireless sensornetworks has been a hot topic among both industrial and academiccommunities [1]-[4]. Energy-efficient designs are essential for wirelesssensor networks, especially for networks with energy-constraint sensors.The energy consumption of a wireless node in communications mainlyconsists of three parts: the RF energy cost for packet transmitting andreceiving, and the energy cost for packet processing.

It is desirable to minimize the total energy consumption ofaccomplishing a set of flow transmissions in wireless sensor networks,by adopting the technology of network coding (NC). Specifically, for awireless network with multiple unicast traffic-flows to be delivered, bycarefully assigning the traffic-flow among different paths and exploringthe chances of NC, one can reduce the times of packet relaying andtransmission, leading to a decreased energy cost.

NC was originally proposed in [5] to boost network throughputs. The keyidea is that different from traditional packet relay operations of“store and forward”, NC allows the relay node to encode packets beforeforwarding. Consider a two-way-relay network in FIG. 1. Nodes A and Bhave packets to exchange with the help of relay node R. If node Rperforms the simple “store and forward” operation, then four unicasttransmissions (Links 1, 2, 3, and 4 in FIG. 1) are required. Thus, thetotal energy consumption includes four times of packet transmitting andreceiving. However, by encoding the packets of nodes A/B andbroadcasting the coded packet (Link 5 in FIG. 1), NC only needs threetransmissions to accomplish the packet exchange. Thus, with NC the totalenergy consumption includes three times of packet transmitting and twotimes of packet receiving.

It is interesting to investigate how the NC technology improves theenergy efficiency in wireless networks. Ref. [6] analyzed the benefitsof NC in terms of energy efficiency under two scenarios: singlemulticast session and multiple unicast sessions. Network coding-awarerouting refers to the routing protocol which can automatically seekcoding opportunities on all available paths.

Among researches on energy-efficient schemes adopting NC, [7] proposed amechanism by detecting potential coding opportunities under two-hopcoding conditions in energy-constrained wireless networks. Ref. [8]combined NC with the connected dominating set and proposed a scheme toreduce energy consumption in Ad Hoc networks. Ref. [1] proposed LEACHthat utilizes randomized rotation of local cluster base stations toevenly distribute the energy load among the sensors in the network. Anew power-aware routing protocol was presented in [2] to maximize thelifetime of wireless node and minimize overall transmission power foreach connection request. Ref. [3] proposed a cluster based energyefficient routing algorithm (CBER) that elects cluster head based onnodes near to the optimal cluster head distance and residual energy ofthe nodes. Ref. [4] proposed a new framework for energy management intime division multiple access- (TDMA-)based wireless mobile networks(WMNs) to support energy efficient communications. However, the aboverouting schemes did not take the benefits brought by NC into account.

The first implementation of NC in real wireless networks, COPE, wasproposed in 2006 to achieve higher unicast throughput for wirelesssensor networks [10]. However, COPE simply seeks for codingopportunities in single hop, which greatly limits the performance of NC.Ref [9] analyzed the throughput benefits brought by NC from acentralized perspective, and discussed the tradeoff between wirelessinterference and coding opportunities. Ref. [11] proved that the energygain is upper bounded by 3. Ref. [12] analyzed the energy minimizationfor lifetime constrained wireless networks and the tradeoff betweencoding opportunities and network lifetime. Ref [13] showed that inmulti-rate wireless networks seeking more coding opportunities withoutexploiting multi-rate feature may lead to selecting low-rate links fortransmission and thus compromise the performance gain andenergy-efficient brought by NC.

Recently, centralized analysis and designed schemes also attracts muchattention. Ref [14] proposed a new framework and an online flow-basedrouting approach to support energy-efficient management in wireless meshnetworks. Ref. [15] proposed two algorithms to minimize the power ofintegrated chassis and linecards that are used while putting the idleones into sleep under constraints of link utilization and packet delay.

Although there have been existing techniques for NC-aware routing, it isadvantageous to have a novel technique improved over existing ones infurther energy reduction and further reduction in time costs. There is aneed in the art for such improved technique.

SUMMARY OF THE INVENTION

In this work, an energy efficient coding-aware scheme (EECAS) isdeveloped. The EECAS provides a novel energy efficient scheme thatincludes a NC-aware traffic-flow assignment and a TDMA-based mediaaccess control (MAC) scheduling strategy. To the best of the inventors'knowledge, this work is the first attempt to combine NC-aware routingand TDMA-based MAC protocol for energy-efficient design in wirelesssensor networks.

The present invention is developed based on the EECAS. An aspect of thepresent invention is to provide a method for scheduling packettransmission among plural nodes. The nodes employ two-way packetrelaying in communication among themselves.

The method comprises a step of, based on a set of user traffic-flowdemands, determining a NC-aware traffic-flow assignment for routing thepacket transmission among the nodes in the presence of NC. Inparticular, the NC-aware traffic-flow assignment minimizes a totalenergy consumption of all the nodes in delivering packets to meet theuser traffic-flow demands. The method further comprises a step ofdetermining a TDMA-based MAC schedule that minimizes a total number oftimeslots required by all the nodes for transmitting the packets whileaccomplishing the NC-aware traffic-flow assignment.

Other aspects of the present invention are disclosed as illustrated bythe embodiments hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an example of a network having a two-way relay structure, theexample being used for illustrating the disclosed routing method.

FIG. 2 is a conflict graph G of the network of FIG. 1.

FIG. 3 is a conflict graph G_(b) with broadcast links of the network ofFIG. 1.

FIG. 4 is a 6-node wireless network with three traffic demands, thenetwork being used to obtain simulation results for evaluating theperformance of the disclosed routing scheme.

FIG. 5 shows the total energy consumption against the amount of trafficdemand x according to simulation results of the first environment.

FIG. 6 shows the total coded traffic against the amount of trafficdemand x according to simulation results of the first environment.

FIG. 7 shows the performance gain against the amount of traffic demand xaccording to simulation results of the first environment.

FIG. 8 shows the total time cost against the amount of traffic demand xaccording to simulation results of the first environment.

FIG. 9 shows the total energy consumption against the amount of trafficdemand y according to simulation results of the second environment.

FIG. 10 shows the total coded traffic against the amount of trafficdemand y according to simulation results of the second environment.

FIG. 11 shows the performance gain against the amount of traffic demandy according to simulation results of the second environment.

FIG. 12 shows the total time cost against the amount of traffic demand yaccording to simulation results of the second environment.

FIG. 13 depicts the steps for scheduling packet transmission accordingto an exemplary embodiment of the present invention.

DETAILED DESCRIPTION

With the basic idea of improving energy-efficiency of wireless sensornetworks by exploring NC opportunities, the present invention providesan EECAS for a wireless network such as a wireless sensor network. Basedon the NC-aware routing analytical framework proposed in [9], we firstformulate an optimization model, which is called as a minimum energyconsumption model (MECM), to minimize the energy consumption foraccomplishing a set of flow transmissions. Thereafter, given the optimalflow assignment of the MECM, we provide a minimum timeslots model (MTM),which leads to a TDMA-based scheduling strategy at the MAC layer.

Specifically, the EECAS comprises the following two procedures.

-   -   Procedure 1: Given a specific network topology and a set of user        traffic-flow demands, we formulate an optimization model, the        MECM, in which the objective function is to minimize the total        energy consumption of packets delivering to meet the user        demands, and the constraints are given by NC rules, the flow        balance on nodes, and so on. By solving the model, we can obtain        an optimal NC-aware traffic-flow assignment.    -   Procedure 2: Given the traffic-flow assignment in Procedure 1,        we design an optimal TDMA-based MAC scheduling strategy to        fulfill the flow transmissions. Specifically, we formulate an        optimization model, viz., the MTM with the target of minimizing        total timeslots.

The main thrust of our work is that we combine the NC-aware routing andTDMA-based MAC protocol to develop an energy efficient scheme, in whichwe explore the network-coding opportunities to reduce energyconsumption. By adopting the first order radio model [1], the energyconsumption of accomplishing a set of flow transmissions can be computedand then minimized. Simulation results validate the performance of EECASin terms of both energy efficiency and time cost.

It is worthwhile to note that EECAS can be implemented under theframework of software-defined network, which is a promising networkarchitecture that decouples the control and data planes to provide anintelligent approach for future wireless networks.

A. Basic Concepts and Notations

Our target is to minimize the overall energy consumption of all nodesfor accomplishing multiple unicast traffic-flow demands in a wirelesssensor network, by introducing the technique of NC. We first presentsome basic concepts and notations in this section.

A.1 First Order Radio Model

According to the first order radio model [1], the energy consumption ofa wireless node mainly consists of three parts: RF energy cost forpackets transmitting (E_(sd)), packets receiving (E_(re)) and energycost for packets processing (E_(cd)):

E _(sd)(k,d)=E _(e) ×k+E _(a) ×k×d ²   (1)

E _(re)(k)=E _(e) ×k   (2)

E _(cd)(k)=E _(c) ×k   (3)

where E_(e) (unit: nJ/bit) denotes the radio energy consumption for eachbit of the transmitter or receiver circuit, R_(a) (unit: nJ/bit/m²)denotes energy consumption for each bit of the transmit amplifier andE_(c) (unit: nJ/bit) denotes the energy consumption for packetsprocessing (i.e. packets coding) of each bit. In (1)-(3), k denotes theamount of traffic delivered, and d is the transmission distance.

Note that in the transmission of the network-coded packets, theparameter of transmission distance d is equal to the maximum distance oftwo unicast links. In addition, the amount of traffic k in transmittingand receiving includes both the unicast and the broadcast packets.

A.2 Network Coding Rule

The EECAS only considers the two-way-relay coding structure as shown inFIG. 1. In general, if a node has n adjacent links, there exist at mostC_(n) ² coding opportunities.

A.3 Wireless Interference and Feasible States

We use a conflict graph G=(V,E) to describe the wireless interference ofa wireless sensor network. Each link (i.e. a transmitter and receiverpair) is modeled as a vertex j∈V. Edges, on the other hand, model thewireless interference relationships among the links. An edge e∈E betweentwo vertices means that they are within interference range of each otherand could not be active simultaneously. FIG. 2 shows the conflict graphof the network of FIG. 1, where links 1, 2, 3, 4 interfere with eachother. It is worthwhile to note that the reverse direction of one linkbetween two nodes is considered as another link in our model.

Note that NC requires a broadcast link, we next introduce the concept ofconflict graph G_(b)=(V_(b),E_(b)) with broadcast links to describe theinterference relationships among both unicast and broadcast links. Inthe expression, V_(b) denotes the set of both unicast and broadcastlinks, and E_(b) denotes the edge set between links. It is easy to seethat in G_(b) we can treat a broadcast link as an extra unicast linkfrom the perspective of channel competition. FIG. 3 shows the conflictgraph with broadcast links of the network shown in FIG. 1, in which anextra node, link 5 is added to reflect the network-coded broadcasttransmission, and links 1, 2, 3, 4, 5 interfere with each other.

In a TDMA-based scheduling scheme, time is divided into timeslots thatare assigned to feasible states of the network. Given the conflict graphwith broadcast links of the network, the feasible states are theindependent sets of the conflict graph. Let s_(j)∈{0,1} denote the stateof link j, where s_(j)=1 if the link j is active (transmitting) ands_(j)=0 if the link j is idle. The feasible state of the overall networkcan be denoted by s=s₁s₂ . . . Note that s_(j) and s_(k) cannot both be1 simultaneously if links j and k are within an interference range witheach other. Let S denote the set of all feasible states and t_(s)denotes the timeslots assigned to state s.

Table I lists some of notations used in this work.

TABLE I Notations used herein. Notation Definition K Demand k D Demandsset N Nodes set o(k) Source node of demand k w(j) Transmitting node oflink j R^(k) Set of available paths for demand k u_(R) ^(k) Amount oftraffic on path R for demand k q_(k) Amount of traffic for demand k jReverse link of link j E⁺ (i), E⁻ (i) Sets of incoming and outgoinglinks of node i m_(i) ^(j), m_(i) ^({j1, j2}) Transmitting traffic atnode i on link j and {j₁, j₂} d_(j) Transmitting distance of link jE_(i) Total energy consumption of node i t_(s) Timeslot of feasiblestate s v_(j) Transmitting rate of link j

B. Energy Efficient Coding-Aware Scheme

We next present our energy efficient coding-aware schemes including theMECM and the MTM. Specifically, we first formulate the target ofminimizing energy consumption as the detailed objective functions.Afterward, we construct an optimization model, the MECM, to obtain anoptimal traffic-flow assignment. According to this assignment, anotheroptimization model, the MTM, is built up to obtain a TDMA-based MACscheduling strategy. Finally, this energy efficient scheme is formed toaccomplish all user traffic-flow demands.

B.1 Problem Formulation

Consider a general wireless sensor network in which there are z unicastuser traffic-flow demands and each demand is to transmit certain amountof data from one node to another. For instance, demand k is to transmittraffic of amount q_(k) from node a to node b. To accomplish all demandswith the minimum consumed energy, the objective function is

F=min(ΣE _(i)), ∀i∈N   (4)

where E_(i) denotes the energy consumption of node i, and ΣE_(i) is thetotal energy consumption of all nodes in the network.

For each user demand k, we need to select available paths from sourcenode to destination node based on routing metrics such as ETX [16], andin this way we can avoid adopting paths with low efficiency beforehand.

The following sections describe the detailed two steps of achievingenergy efficient scheme by two models: the MECM and the MTM.

B.2 MECM-Minimum Energy Consumption Model

The EECAS targets to minimize the total energy consumption in wirelesssensor network given user traffic-flow demands and network conditions.We next formulate the following optimization problem:

$\begin{matrix}{\mspace{79mu} {{Objective}\mspace{14mu} {function}\mspace{14mu} {{◯1}:}}} & \; \\{\mspace{79mu} {{F = {{\min \left( {\Sigma \; E_{i}} \right)}\mspace{14mu} {\forall{i \in N}}}}\mspace{20mu} {{subject}\mspace{14mu} {to}}}} & (5) \\{\mspace{79mu} {{{\sum\limits_{R \in R^{k}}\; u_{R}^{k}} = {q_{k}\mspace{14mu} {\forall{k \in D}}}},}} & (6) \\{\mspace{79mu} {{m_{i}^{\{{j_{1},j_{2}}\}} \leq {\sum\limits_{k \in D}\; {\sum\limits_{{R \in R^{k}},{{j_{2}j_{1}} \in R}}\; {u_{R}^{k}\mspace{14mu} {\forall j_{1}}}}}},{j_{2} \in {E^{+}(i)}},{i \in N},}} & (7) \\{{m_{i}^{\{ j\}} \leq {{\sum\limits_{{k \in D},{{o{(k)}} = i}}\; {\sum\limits_{{R \in R^{k}},{j \in R}}\; u_{R}^{k}}} + {\sum\limits_{j_{1} \in {E^{-}{(i)}}}\; \left\lbrack {{\sum\limits_{k \in D}\; {\sum\limits_{{R \in R^{k}},{{j_{1}j} \in R}}\; u_{R}^{k}}} - m_{i}^{\{{j,\overset{\_}{j_{1}}}\}}} \right\rbrack}}}\mspace{20mu} {{\forall{j \in {E^{+}(i)}}},{i \in N},}} & (8) \\{\mspace{79mu} {{E_{i} = {E_{i{({sd})}} + E_{i{({re})}} + {E_{i{({cd})}}\mspace{14mu} {\forall{i \in N}}}}},}} & (9) \\{{E_{i{({sd})}} = {{\sum\limits_{j \in {E^{+}{(i)}}}\; {\left( {E_{e} + {E_{a} \cdot d_{j}^{2}}} \right) \times m_{i}^{j}}} + {\sum\limits_{{\{{j_{1},j_{2}}\}} \in {E^{+}{(i)}}}\; {\left( {E_{e} + {E_{a} \cdot {\max \left( {d_{j_{1}},d_{j_{2}}} \right)}^{2}}} \right) \times m_{i}^{\{{j_{1},j_{2}}\}}}}}}\mspace{20mu} {{\forall{j \in {E^{+}(i)}}},{\forall{\left\{ {j_{1},j_{2}} \right\} \in {E^{+}(i)}}},{i \in N},}} & (10) \\{\mspace{79mu} {{E_{i{({re})}} = {E_{e} \cdot \left( {{\sum\limits_{j \in {E^{-}{(i)}}}\; m_{i_{1}:{i_{1} \in {w{(j)}}}}^{\{ j\}}} + {\sum\limits_{j_{1}|{j_{2} \in {E^{-}{(i)}}}}\; m_{{i_{2}:{i_{2} \in {w{(j_{1})}}}},{w{(j_{2})}}}^{\{{j_{1},j_{2}}\}}}} \right)}}\mspace{20mu} {{\forall{j \in {E^{-}(i)}}},{\forall{\left\{ {j_{1},j_{2}} \right\} \in {E^{-}(i)}}},{i \in N},\mspace{20mu} {and}}}} & (11) \\{\mspace{79mu} {{E_{i{({cd})}} = {{E_{c} \cdot \left( {\sum\limits_{{({j_{1},j_{2}})} \in {E^{+}{(i)}}}\; m_{i}^{\{{j_{1},j_{2}}\}}} \right)}\mspace{14mu} {\forall{\left\{ {j_{1},j_{2}} \right\} \in {E^{+}(i)}}}}},{i \in {N.}}}} & (12)\end{matrix}$

EQN. (6) denotes the total traffic of demand k∈D distributed over allavailable paths R^(k) must be equal to traffic amount q_(k). EQN. (7)determines the maximum amount of coded traffic m_(i) ^({j) ¹ ^(,j) ²^(}) that can be broadcast on outgoing links {j₁,j₂} should be less thantotal incoming traffic on link j₁ j₂ or j₂ j₁ at node i. EQN. (8)denotes the total amount of traffic m_(i) ^({j}) that is unicast onoutgoing link j at node i can be divided into two parts: traffic thatoriginates at node i with outgoing link j and traffic of incoming node iwith outgoing link j that could not be coded. EQNS. (9)-(12) aredefinitions of energy consumption according to first order radio model.EQN. (10) denotes the total energy consumption E_(i(sd)) in transmittingpackets at node i includes both unicast and broadcast transmission. Inbroadcast transmission, the parameters of transmission distance must beequal to max(d_(j) ₁ ,d_(j) ₂ ). EQN. (11) denotes that the total energyconsumption E_(i(re)) in receiving packets at node i includes both theunicast and broadcast received. EQN. (12) denotes energy consumption ofpackets coding.

B.3 Analysis of Benefit Brought by Network Coding

We next analyze the interactions between the benefits in terms of energyconsumption and the coding opportunities in MECM.

As mentioned above, NC may reduce energy consumption in a two-way-relaypacket exchange process. More specifically, one time of energyconsumption of packet transmitting is reduced while one time of energyconsumption of packet coding is added. Thus, the reduction of energyconsumption E_(b) brought NC in a two-way-relay packets exchange couldbe denoted by

E _(b) =E _(e) ×k+E _(a) ×k×d ² −E _(c) ×k.   (13)

EQN. (13) shows that one bit of packet coding could reduceE_(e)+E_(a)×d²−E_(c) unit of energy.

Table II lists the typical parameters setting in the first order radiomodel. It is easy to see that one bit of coded traffic could reduce 55nJ of energy consumption for a broadcast with transmitting distance of10 m. With more coding opportunities in a large-scale wireless network,NC could bring higher energy-efficiencies. Thus in MECM, the target ofminimizing total energy consumption is equivalent to the target ofmaximizing coding opportunities.

TABLE II Parameters Setting Parameter Setting E_(e): energy consumptionfor the transmitter or receiver 50 nJ/bit circuitry E_(a): energyconsumption for the transmit amplifier 100 pJ/bit/m2 E_(c): energyconsumption for packet coding 5 nJ/bit

By solving the MECM, we obtain an optimal traffic-flow assignment m_(i)^(j). However, without a MAC protocol it is still not enough to form acomplete energy-efficient scheme. The following TDMA-based schedulingstrategy is proposed for this purpose.

B.4 MTM—Minimum Timeslots Model

At the MAC layer, we divide time into timeslots and introduce aTDMA-based MAC protocol to fulfill a complete energy efficient scheme byminimizing the total time cost while accomplishing the traffic-flowassignment generated by the MECM.

Let v_(j) denote the effective transmission rate of link j. The timeslotfor link j to accomplish its own traffic demand m_(i) ^(j) is m_(i)^(j)/v_(j). It is easy to see that the total timeslots for link j totransmit m_(i) ^(j) amount of data should be equal to the totaltimeslots assigned to the feasible states in which it is active. Here,we minimize the total time cost of all feasible states whileaccomplishing all traffic m_(i) ^(j) of each link j. We formulate theoptimization problem:

$\begin{matrix}{{Objective}\mspace{14mu} {function}\mspace{14mu} {{◯2}:}} & \; \\{{F = {\min {\sum\limits_{s \in S}\; t_{s}}}}{{subject}\mspace{14mu} {to}}} & (14) \\{\frac{m_{i}^{j}}{v_{j}} = {\sum\limits_{{s:s_{j}} = 1}\; {t_{s}\mspace{14mu} {\forall{j \in V_{b}}}}}} & (15)\end{matrix}$

where (s: s_(j)=1) represents the feasible state where s_(j)=1.

The effective transmission rate of broadcast link pair {j₁,j₂} satisfiesa condition v_({j) ₁ _(,j) _(2}) =min(v_(j) ₁ ,v_(j) ₂ ) due to thebroadcast nature.

Both the MECM and the MTM are linear and can be solved by using standardoptimization tools.

C. Performance Evaluation

We next evaluate the performance of EECAS in terms of both energyefficiency and time cost. We consider a 6-node wireless network as shownin FIG. 4. Each link between adjacent nodes represents a communicationpair. Three user traffic-flow demands exist as follows: {circle around(1)} node A→node F; {circle around (2)} node D→node A; {circle around(3)} node F→node B. All available paths based on the shortest path ofeach demand is shown in the figure. In this network scenario, NCopportunities exist at node B, C, E. The NC incurred broadcast link ofnode B corresponds to B→A/C; the broadcast link of node C corresponds toC→B/F; the broadcast link of node E corresponds to E→B/F. The distancebetween all adjacent nodes is 10 meters, and the transmission rate ofall links is equal. The IEEE 802.11b protocol with the transmission rateof 11 Mbps is adopted in our simulation. The interference relationshipof this network is that one link is within interference range withanother link only if they contain one same node. For instance, link A-Bis within interference range with link B-C, while link A-B is withoutinterference range with link C-D.

The traffic amount of the three demands are denoted by x, y, z. First,we use a set of random values to demonstrate the routing strategygenerated by the EECAS. Let (x, y, z)=(40,20,30) (unit: Mb). By theMECM, the total energy consumption on all nodes is 24.75 J under theoptimal traffic assignment. Tables III and IV list the amount of codedtraffic and the assignment of traffic-flow among different paths.

TABLE III Amount Of Coded Traffic Broadcast link Broadcast linkBroadcast link B→A/C C→B/F E→B/F Amount of Coded 30 Mb 15.79 Mb 4.21 Mbtraffic

TABLE IV Distribution of Traffic Flow in Different Paths Demand {circlearound (1)} Demand {circle around (2)} Demand {circle around (3)} Path1:Path2: Path: Path1: Path2: A-B-C-F A-B-E-F D-C-B-A F-C-B F-E-B 32.65 Mb7.35 Mb 30 Mb 15.79 Mb 4.21 Mb

By the MTM we can obtain the amount of traffic m_(i) ^(j) of each linkand the timeslots t_(s) assigned to each feasible state, leading to anoptimal energy efficient scheme that minimizes the total energyconsumption. The detailed statics are omitted here due to limited space.

In order to validate the benefits of the EECAS, we compare theperformance of the following three routing schemes in terms of bothenergy efficiency and time cost.

(a) CR (Common Routing)

(b) CAR (Coding-Aware Routing)

(c) EECAS (Energy-Efficient Coding-Aware Scheme)

CR refers to as the common routing without NC. CAR refers to thetraditional coding aware routing [9] that aims at maximizing networkthroughputs. We next conduct two sets of experiments to investigate theperformance of the three algorithms. The amount of total coded trafficrefers to the sum of all coded traffic in each node.

C.1 Results for the First Simulation Environment

In the first simulation environment, x ranges from 1-50, y=20, z=30(unit: Mb). Simulation results are shown in FIGS. 5-8.

FIG. 5 shows the total energy consumption of three routing schemes withvariation of x. The EECAS costs the least energy compared to CR and CAR.FIG. 6 shows the total coded traffic in all nodes. Obviously, the totalcoded traffic of CR is zero without NC. The amount of coded traffic ofthe EECAS rises with the increase of x and reaches the maximum amount of50 Mb when x=30. Traffic of demand 1 could be coded with traffic ofdemand 2 and 3, while traffic of demand 2 and 3 could not be coded witheach other. Thus when x=30 Mb, traffic of demand 1 all transmits throughpath A-B-C-F and traffic of demand 3 all transmits through path F-C-B.Thus traffic of demand 1 could be coded twice: coded with traffic ofdemand 2 at node B with amount of 20 Mb and coded with traffic of demand3 at node C with amount of 30 Mb. CAR has less coded traffic compared tothe EECAS. FIG. 7 shows the performance gain in energy consumption ofthe EECAS. The EECAS reduces at most 11% of energy compared to CR, and6% compared to CAR when the performance gain brought by NC reaches thetop when x=30.

We also compare the total time cost of CR and EECAS. Note that using NCcould bring two opposite effect on the total time cost of EECAS. Thefirst aspect is that NC itself could effectively reduce time cost asshown in FIG. 1. The second aspect is that the greedy pursuit ofmaximizing coding opportunities and does not consider the tradeoffbetween wireless interference and coding opportunities would converselycause link blocking and throughput degradation. The total time cost ofEECAS is determined by these two aspects. From FIG. 8, we can see thatthe EECAS actually costs less time than CR in general. It is because thepositive effect of NC always exists when x ranges from 1-60. On theother hand, when x ranges from 1-30, the negative effect of using NC hasgreat influence. When x ranges from 30-60, no more coding opportunitiesincreases thus the negative effect of NC is weakened.

C.2 Results for the Second Simulation Environment

The second simulation environment: y ranges from 1-60, x=20, z=30 (unit:Mb). Simulation results are shown in FIGS. 9-12.

The total energy consumption with variation of y is similar to FIG. 5.The difference is that the starting point of three protocols may notcoincidence as in FIG. 5, because there already exists NC when y=0.Likewise, the starting point of FIG. 10 dose not start from originalpoint. The total coded traffic reaches 40 Mb when y=20 as 20 Mb trafficof demand 1 is coded twice in node B, C. FIG. 12 shows the performancegain in energy consumption. Similarly, EECAS reduces at most 11% ofenergy compared to CR and 6% compared to CAR when the performance gainbrought by NC reaches the top when y=20.

The total time cost with variation of y can be seen in FIG. 12. When yranges from 1-20, the time cost of CR and EECAS is equal. As explainedin FIG. 8, when y ranges from 1-20, the negative effect of using NC hasgreat influence. When y ranges from 20-60, no more coding opportunitiesincreases thus the negative effect of NC is weakened and the curve tendsto be gentle.

From the simulation results above we can see that the EECAS costs muchless energy than CR and CAR which indicates that coding opportunitiesbrings distinct benefit in energy consumption. The EECAS can reduce atmost 11% of energy consumption compared to CR and at most 6% compared toCAR in the network. Moreover, the EECAS can effectively reduce totaltime cost compared to CR due to NC.

D. The Present Invention

An aspect of the present invention is to provide a method for schedulingpacket transmission among plural nodes in a wireless network. Inparticular, the method is based on the EECAS as disclosed above.

The method is exemplarily illustrated as follows with the aid of FIG.13, which depicts the method steps according to an exemplary embodimentof the present invention. Based on a set of user traffic-flow demands, aNC-aware traffic-flow assignment for routing the packet transmissionamong the nodes in the presence of NC is determined in a step 1310. Inparticular, the NC-aware traffic-flow assignment minimizes a totalenergy consumption of all the nodes in delivering packets to meet theuser traffic-flow demands. Thereafter, a TDMA-based MAC schedule isdetermined in a step 1320. The schedule minimizes a total number oftimeslots required by all the nodes for transmitting the packets whileaccomplishing the NC-aware traffic-flow assignment. The determinedschedule provides a scheme for scheduling the packet transmission amongthe nodes.

In general, each of the nodes is implemented with one or more computingprocessors for realizing computing and control functions. Preferably,the NC-aware traffic-flow assignment for the nodes is determined bynumerically minimizing an objective function representing the totalenergy consumption of the nodes under a plurality of constraints. Theplurality of constraints includes a first constraint that a total energyconsumption in transmitting and receiving packets at any node i includesamounts of energy consumed in unicast transmission and in broadcasttransmission. Other constraints may be included in the plurality ofconstraints and are given in Section B.2 above.

In one embodiment, the objective function is provided by (5) and theplurality of constraints is a set of equations given by (6)-(12).

Preferably, the TDMA-based MAC schedule is determined by finding a states=s₁s₂ . . . in S such that t_(s) subject to a constraint given by (14)is minimum over all the feasible states in S.

The disclosed method is implementable in a wireless network comprisingplural nodes. The nodes are collectively configured to employ two-waypacket relaying in communication among the nodes, and to schedule packettransmission among the nodes according to any of the embodimentsdisclosed herein.

The method is particularly advantageous for use in a wireless sensornetwork. In the wireless sensor network, each of the nodes is a sensorfor performing a certain kind of sensing or measurement, and the sensoris further configured to be wirelessly communicable with another sensorin the network.

The embodiments disclosed herein may be implemented using generalpurpose or specialized computing devices, computer processors, orelectronic circuitries including but not limited to digital signalprocessors, application specific integrated circuits, field programmablegate arrays, and other programmable logic devices configured orprogrammed according to the teachings of the present disclosure.Computer instructions or software codes running in the general purposeor specialized computing devices, computer processors, or programmablelogic devices can readily be prepared by practitioners skilled in thesoftware or electronic art based on the teachings of the presentdisclosure.

The present invention may be embodied in other specific forms withoutdeparting from the spirit or essential characteristics thereof Thepresent embodiment is therefore to be considered in all respects asillustrative and not restrictive. The scope of the invention isindicated by the appended claims rather than by the foregoingdescription, and all changes that come within the meaning and range ofequivalency of the claims are therefore intended to be embraced therein.

What is claimed is:
 1. A method for scheduling packet transmission amongplural nodes, the nodes employing two-way packet relaying incommunication among themselves, the method comprising: based on a set ofuser traffic-flow demands, determining a network coding (NC)-awaretraffic-flow assignment for routing the packet transmission among thenodes in the presence of NC, wherein the NC-aware traffic-flowassignment minimizes a total energy consumption of all the nodes indelivering packets to meet the user traffic-flow demands; anddetermining a time division multiple access (TDMA)-based media accesscontrol (MAC) schedule that minimizes a total number of timeslotsrequired by all the nodes for transmitting the packets whileaccomplishing the NC-aware traffic-flow assignment.
 2. The method ofclaim 1, wherein the NC-aware traffic-flow assignment is determined bynumerically minimizing an objective function representing the totalenergy consumption of the nodes under a plurality of constraints, theplurality of constraints including a first constraint that a totalenergy consumption in transmitting and receiving packets at any node iincludes amounts of energy consumed in unicast transmission and inbroadcast transmission.
 3. The method of claim 2, wherein the pluralityof constraints further includes a second constraint that at the node i,a maximum amount of coded traffic m_(i) ^({j) ¹ ^(,j) ² ^(}) broadcaston outgoing links {j₁,j₂} is less than a total incoming traffic on alink j₁ j₂ or j₂ j₁ where j denotes a reverse link of any link j.
 4. Themethod of claim 2, wherein the first plurality of constraints furtherincludes a third constraint that at the node i, a total amount oftraffic m_(i) ^({j}) that is unicast on an outgoing link j is the sumof: a first amount of traffic that originates at the node i and istransmitted on the outgoing link j; and a second amount of incomingtraffic sent to the node i and then transmitted on the outgoing link jwithout coding.
 5. The method of claim 1, wherein the NC-awaretraffic-flow assignment is determined by numerically minimizing anobjective function, denoted as F₁ and given by F₁=ΣE_(i) ∀i∈N, under aplurality of constraints given by: $\begin{matrix}{\mspace{79mu} {{{\sum\limits_{R \in R^{k}}\; u_{R}^{k}} = {q_{k}\mspace{14mu} {\forall{k \in D}}}};}} \\{\mspace{79mu} {{m_{i}^{\{{j_{1},j_{2}}\}} \leq {\sum\limits_{k \in D}\; {\sum\limits_{{R \in R^{k}},{{j_{2}j_{1}} \in R}}\; {u_{R}^{k}\mspace{14mu} {\forall j_{1}}}}}},{j_{2} \in {E^{+}(i)}},{{i \in N};}}} \\{\mspace{79mu} {{m_{i}^{\{ j\}} \leq {{\sum\limits_{{k \in D},{{o{(k)}} = i}}\; {\sum\limits_{{R \in R^{k}},{j \in R}}\; u_{R}^{k}}} + {\sum\limits_{j_{1} \in {E^{-}{(i)}}}\; \left\lbrack {{\sum\limits_{k \in D}\; {\sum\limits_{{R \in R^{k}},{{j_{1}j} \in R}}\; u_{R}^{k}}} - m_{i}^{\{{j,\overset{\_}{j_{1}}}\}}} \right\rbrack}}}\mspace{20mu} {{\forall{j \in {E^{+}(i)}}},{{i \in N};}}}} \\{\mspace{79mu} {{E_{i} = {E_{i{({sd})}} + E_{i{({re})}} + {E_{i{({cd})}}\mspace{14mu} {\forall{i \in N}}}}};}} \\{{E_{i{({sd})}} = {{\sum\limits_{j \in {E^{+}{(i)}}}\; {\left( {E_{e} + {E_{a} \cdot d_{j}^{2}}} \right) \times m_{i}^{j}}} + {\sum\limits_{{\{{j_{1},j_{2}}\}} \in {E^{+}{(i)}}}\; {\left( {E_{e} + {E_{a} \cdot {\max \left( {d_{j_{1}},d_{j_{2}}} \right)}^{2}}} \right) \times m_{i}^{\{{j_{1},j_{2}}\}}}}}}\mspace{20mu} {{\forall{j \in {E^{+}(i)}}},{\forall{\left\{ {j_{1},j_{2}} \right\} \in {E^{+}(i)}}},{{i \in N};}}} \\{\mspace{79mu} {{E_{i{({re})}} = {E_{e} \cdot \left( {{\sum\limits_{j \in {E^{-}{(i)}}}\; m_{i_{1}:{i_{1} \in {w{(j)}}}}^{\{ j\}}} + {\sum\limits_{j_{1}|{j_{2} \in {E^{-}{(i)}}}}\; m_{{i_{2}:{i_{2} \in {w{(j_{1})}}}},{w{(j_{2})}}}^{\{{j_{1},j_{2}}\}}}} \right)}}\mspace{20mu} {{\forall{j \in {E^{-}(i)}}},{\forall{\left\{ {j_{1},j_{2}} \right\} \in {E^{-}(i)}}},{{i \in N};}}\mspace{20mu} {and}}} \\{\mspace{79mu} {{E_{i{({cd})}} = {{E_{c} \cdot \left( {\sum\limits_{{({j_{1},j_{2}})} \in {E^{+}{(i)}}}\; m_{i}^{\{{j_{1},j_{2}}\}}} \right)}\mspace{14mu} {\forall{\left\{ {j_{1},j_{2}} \right\} \in {E^{+}(i)}}}}},{{i \in N};}}}\end{matrix}$ where: j denotes a reverse link of any link j; k denotes ademand; E_(i) is the energy consumption of a node i selected from thenodes, and ΣE_(i) is the total energy consumption of all the nodes; o(k)denotes a source node of the demand k; R^(k) is a set of available pathsfor the demand k; u_(R) ^(k) is an amount of traffic on any path R forthe demand k; q_(k) is an amount of traffic for the demand k; E⁺(i) is aset of incoming links of the node i; E⁻(i) is a set of outgoing links ofthe node i; w(j) denotes a transmitting node of any link j; m_(i) ^(j)is a transmitting traffic at the node i on the link j; m_(i) ^({j) ¹^(,j) ² ^(}) is a transmitting traffic at the node i on the link{j₁,j₂}; d_(j) is a transmitting distance of the link j; D is a demandsset; and N is a nodes set.
 6. The method of claim 5, wherein theTDMA-based MAC schedule is determined by determining a state s=s₁s₂ . .. in S, a set of all feasible states, such that t_(s), subject to${\frac{m_{i}^{j}}{v_{j}} = {\sum\limits_{{s:s_{j}} = 1}\; {t_{s}\mspace{14mu} {\forall{j \in V_{b}}}}}},$is minimum over all the feasible states in S, where: t_(s′) denotes thenumber of timeslots assigned to a state s′ in S; s_(j) in s denotes astate of the link j, where s_(j)=1 if the link j is active, and s_(j)=0if the link j is idle; (s: s_(j)=1) represents the state s havings_(j)=1; v_(j) is an effective transmission rate of the link j; andV_(b) denotes a set of both unicast and broadcast links in an entiretyof the nodes.
 7. A wireless network comprising plural nodes, wherein thenodes are collectively configured to employ two-way packet relaying incommunication among the nodes, and to schedule packet transmission amongthe nodes according to the method of claim
 1. 8. The wireless network ofclaim 7, wherein each of the nodes is a sensor and the sensor is furtherconfigured to be wirelessly communicable with another sensor, so thatthe wireless network forms a wireless sensor network.
 9. A wirelessnetwork comprising plural nodes, wherein the nodes are collectivelyconfigured to employ two-way packet relaying in communication among thenodes, and to schedule packet transmission among the nodes according tothe method of claim
 2. 10. The wireless network of claim 9, wherein eachof the nodes is a sensor and the sensor is further configured to bewirelessly communicable with another sensor, so that the wirelessnetwork forms a wireless sensor network.
 11. A wireless networkcomprising plural nodes, wherein the nodes are collectively configuredto employ two-way packet relaying in communication among the nodes, andto schedule packet transmission among the nodes according to the methodof claim
 3. 12. The wireless network of claim 11, wherein each of thenodes is a sensor and the sensor is further configured to be wirelesslycommunicable with another sensor, so that the wireless network forms awireless sensor network.
 13. A wireless network comprising plural nodes,wherein the nodes are collectively configured to employ two-way packetrelaying in communication among the nodes, and to schedule packettransmission among the nodes according to the method of claim
 4. 14. Thewireless network of claim 13, wherein each of the nodes is a sensor andthe sensor is further configured to be wirelessly communicable withanother sensor, so that the wireless network forms a wireless sensornetwork.
 15. A wireless network comprising plural nodes, wherein thenodes are collectively configured to employ two-way packet relaying incommunication among the nodes, and to schedule packet transmission amongthe nodes according to the method of claim
 5. 16. The wireless networkof claim 15, wherein each of the nodes is a sensor and the sensor isfurther configured to be wirelessly communicable with another sensor, sothat the wireless network forms a wireless sensor network.
 17. Awireless network comprising plural nodes, wherein the nodes arecollectively configured to employ two-way packet relaying incommunication among the nodes, and to schedule packet transmission amongthe nodes according to the method of claim
 6. 18. The wireless networkof claim 17, wherein each of the nodes is a sensor and the sensor isfurther configured to be wirelessly communicable with another sensor, sothat the wireless network forms a wireless sensor network.